According to Christopher Hughes, arguments from contingency for the existence of a necessary being are standardly held to depend on two crucial assumptions: a contingency-dependence principle (which may be thought to derive from the Principle of Sufficient Reason), and the existence of a sufficiently inclusive being. The burden of Hughes’s contribution to The Puzzle of Existence is to argue that the second assumption can be dispensed with.

Let’s start by seeing what these two assumptions are, and how they fit into standard arguments. A contingency-dependence principle states that any contingent entity must depend for its existence on some entity outside it. (On some broadly Aristotelian theories of modality, including theories often attributed to Medieval philosophers, contingency is defined as this sort of dependence.) The sufficiently inclusive being assumption basically allows that there is a being ‘big enough’ that anything outside it would have to be a necessary being. Thus, for instance, we might argue:

Every contingent being depends for its existence on some being which is not a (proper or improper) part of it. (Contingency-Dependence Principle)

There is a contingent being, The World, of which every contingent being is a part. (Sufficiently Inclusive Being)

Therefore,

The World depends on some non-contingent (i.e. necessary) being.

Therefore,

There is a necessary being.

As we have already seen in this series, some philosophers, including Immanuel Kant and Jacob Ross, respond to arguments from contingency by denying the existence of a sufficiently inclusive being. In terms of the version of the argument just given, we could say that these philosophers hold that, although there are many contingent beings, there is no whole made up of all the contingent beings as parts. According to Hughes, however, this is insufficient to escape the force of the argument from contingency; the argument can be reformulated in the absence of a sufficiently inclusive being.

The idea here is one that will be familiar to most philosophers: plural quantification. This is a formalism introduced by George Boolos for talking about several things without quantifying over sets, collections, sums, etc., of those things. It was said that, without quantifying over sets, one could not formalize such sentences as “some critics only admire each other.” With plural quantification, this is regimented as “There are some critics each of whom admires a person only if that person is one of them, and none of whom admires himself” (p. 103). Thus, Hughes suggests, the following principle can be made to yield a necessary being without requiring the existence of a sufficiently inclusive being:

If any being is contingent, or any two or more beings are (all) contingent, then there is some being outside that being or outside (all) those beings, on which that being or at least one of those beings depends (p. 101).

Given this principle, it appears that we only need the premise “there are some contingent beings” to get the existence of a non-contingent being. We don’t need the existence of ‘The World’ or any such thing.

If Hughes is right, then the contingency-dependence principle is really the heart of the argument. He therefore concludes by discussing the status of this principle. According to Hughes, “Some people have an immediate, strong, and stable intuition that contingent beings, as such, are incapable – singly or jointly – of existing without an external ‘ground'” (p. 105). He holds that people who do have this intuition are at least prima facie justified in being persuaded by the argument from contingency for the existence of a necessary being. However, Hughes reports that he himself has no such intuition, and so is unpersuaded by the argument (p. 108).

I found Hughes’s paper very interesting. I have just two criticisms, one to do with Hughes’s argument itself, and one to do with Hughes’s discussion of the significance of the argument. On the first point, why cannot the denier of sufficiently inclusive beings translate her claim into the language of plural quantification? The claim would go like this:

There are no things such that every contingent being is among them.

Or equivalently:

For any things, there is a contingent being that is not among them.

Admittedly, I can’t figure out how to put this claim into ‘plain English,’ but it is at least not obvious to me that the claim is untenable.

I think this is actually a pretty big problem given Hughes’s argument on pp. 103-104. There, Hughes argues that if Boolos is wrong about the ‘ontological innocence’ of plural quantification, then we need to go ahead and commit to the existence of sets. However, a lot of people accept the set-theoretic version of the claim above, i.e.:

There is no set of which every contingent being is a member.

Indeed, precisely this claim is defended by Ross in the essay immediately preceding Hughes’s! This is an important gap in Hughes’s argument for the irrelevance of sufficiently inclusive entities.

My other complaint is about Hughes’s claim that the argument has little persuasive force because most of those who have the contingency-dependence intuition are already theists. Hughes writes, “All the atheists I know think that something’s being contingent and independent is conceivable and not (even initially) apparently impossible” (p. 107). Again, Hughes should have read Ross, who apparently has the contingency-dependency intuition and tries to escape the conclusion with the very tactic Hughes criticizes. (If all the atheists already reject the contingency-dependence intuition, then who is it that’s supposed to be trying to get out of the conclusion by rejecting sufficiently inclusive entities?) Also, although this is perhaps a merely verbal point, there are those who believe (on the basis of an argument like this one) in a necessary being whom they, for one reason or another (perhaps because it is an impersonal being), prefer not to call ‘God.’

An important question here is exactly what this notion of ‘dependence’ amounts to. I have been reading the contingency-dependence principle as saying something like: if something exists, and it might not have existed, then some other thing must have made it exist. I suspect a lot of atheists do feel the pull of that kind of intuition. Atheists (and others) are welcome to speak up in the comments.

Interestingly, if one thinks that for any two objects there is a mereological sum of them, then there will be at least as many contingent beings as necessary beings. For given any contingent being C and necessary being N, there will be a sum C+N, and that sum is not contingent, so it’s necessary. If one thinks, say due to Platonist mathematical assumptions, that there are too many necessary beings for there to be a plurality of them (there are a bunch of papers arguing that one gets Russell-type paradoxes from supposing a plurality of all abstract beings), then there will be too many contingent beings for a plurality! (I’m being sloppy, of course.)

Alex – Did you mistype? The sum C+N exists only if both C and N exist, so there are possible worlds at which C+N fails to exist, namely, all of those at which C does not exist. Did you mean to say that C+N is not necessary, so it’s contingent?

I agree that if there are too many necessary beings for there to be a plurality of them, and if there is at least one contingent being, and if we accept the sum assumption, then there are too many contingent beings for there to be a plurality of them.

Hi Kenny,
I’m really enjoying your post series. Although I’m not an atheist (I’m agnostic), I’m among those who doesn’t share the intuition behind the contingency-dependence principle. Suppose such a being is a backwardly everlasting being that’s also uncreated and metaphysically independent. If you also have Kripkean origin essentialist intuitions, then you’ll also think such a being can’t depend for something beyond itself, no?

I also worry that we’re picking and choosing our modal intuitions when it comes to contingency arguments. I have modal intuitions that if there is a god, there could’ve been a different god, and no god at all. I suspect those who don’t buy the modal ontological argument agree with me.(I’m assuming we’re talking about a contingency argument aimed to persuade those who don’t have the requisite modal intuitions to buy the modal ontological argument). I suspect those with similar modal intuitions will be sympathetic to at least the epistemic possibility of contingent yet independent beings of the sort sketched above.

Felipe – Interestingly, in James Ross’s Philosophical Theology, there is a version of the ontological argument, attributed to Duns Scotus, that essentially combines your first paragraph with a contingency-dependence principle to yield the conclusion that God exists necessarily. The idea is something like: it is possible that God exists, but it is not possible that God depend on anything else for his existence, therefore there is a possible at which God exists and does not depend on anything else for his existence, hence (by a necessitizied contingency-dependence principle) God exists necessarily at that world, and therefore God exists necessarily at every world. Make what you will of this.

As for your second paragraph, I myself don’t put too much stock in modal intuitions, since my own modal intuitions are inconsistent. Nevertheless, when I don’t have anything better to go on, I do consider fit with more and stronger intuitions to be a point in a theory’s favor.